Triple
T20471196
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Hermite–Minkowski theorem |
E502195
|
entity |
| Predicate | relatedTo |
P37
|
FINISHED |
| Object | Hermite’s constant |
—
|
NE NERFINISHED |
How this triple was built (2 steps)
Every LLM step that produced this triple, in pipeline order — named-entity classification, the disambiguation choices (the exact options shown, with the pick highlighted), and the generated description. The batch + timestamp of each is in the Provenance table below.
NER
Named-entity recognition
gpt-5-mini
Instruction
Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).
Input
Phrase: Hermite’s constant | Statement: [Hermite–Minkowski theorem, relatedTo, Hermite’s constant]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Hermite’s constant Context triple: [Hermite–Minkowski theorem, relatedTo, Hermite’s constant]
-
A.
Hermite constant
chosen
The Hermite constant is a number in each dimension that measures the densest possible lattice sphere packing, playing a central role in the geometry of numbers and lattice theory.
-
B.
Hermite–Minkowski theorem
The Hermite–Minkowski theorem is a fundamental result in algebraic number theory that gives a finiteness bound on the number of number fields of a given degree and discriminant.
-
C.
Koksma–Hlawka inequality
The Koksma–Hlawka inequality is a fundamental result in numerical analysis and discrepancy theory that bounds the error of quasi-Monte Carlo integration by the product of a function’s variation and the discrepancy of the sampling points.
-
D.
Liouville's inequality in Diophantine approximation
Liouville's inequality in Diophantine approximation is a foundational result that gives explicit lower bounds on how closely algebraic numbers can be approximated by rationals, leading to the first examples of transcendental numbers.
-
E.
Hurwitz determinants
Hurwitz determinants are specific determinants constructed from a polynomial’s coefficients that are used to test whether all roots of the polynomial lie in the left half of the complex plane, thereby assessing system stability.
- F. None of above.
- G. Unsure - the case is ambiguous/there is not enough information to decide.
Provenance (2 batches)
The batch behind each pipeline step, in order, with when it ran. Timestamps are batch-level — stages were processed in waves, so the object chain (NER → NED1 → NEDg → NED2) reads in order, but predicate / elicitation batches can sit in a different wave.
| Step | Stage | Batch ID | Status | When |
|---|---|---|---|---|
| creating | Elicitation | batch_69e0b4ae5f1081908768b0c9a3a0bf38 |
completed | April 16, 2026, 10:06 a.m. |
| NER | Named-entity recognition | batch_69e699608d7c8190910217817e789915 |
completed | April 20, 2026, 9:23 p.m. |
Created at: April 16, 2026, 11:33 a.m.